When NHS England’s chief executive, Simon Stevens, was being grilled by MPs the other day, he was momentarily thrown when asked by Anne Marie Morris, the colourful Conservative member for Newton Abbot, whether his optimistic timetable for delivering reform of the health and care system was based on “smoking dope”.

If Chris Wormald, the Department of Health permanent secretary sitting alongside him, allowed himself a snigger at that, he was soon rather more discomfited when questioned on planning for the so-called Dilnot cap on personal liability for social care costs, delayed from 2016 but since repeatedly promised by ministers for April 2020.

Wormald ducked and weaved, but eventually had to resort to saying: “That’s not a question I have a specific answer to here. I will write to the committee.”

It is an odd state of affairs when one of Whitehall’s most senior civil servants is unable to respond directly to the Commons public accounts committee on one of his department’s key policies. But the whole social care picture is in flux after months of growing unrest over the government’s neglect of the sector’s state of crisis, and from here on anything could happen.

Wednesday’s budget should offer us some clues. There is widespread expectation of an emergency injection of cash to “stabilise” the sector in England. A flurry of reports in the past week has put the system’s funding gap in 2017-18 at anything from £1.3bn to £2bn. Although councils are already due to receive an extra £346m for social care (£241m of it redirected from housing), plus up to £630m if they all elect to impose the full 3% special social care levy on council tax (which they won’t), the April rise in the “national living wage” will soak up an estimated two-thirds of all that.

Lest there were any doubt about the need for greater stability in the sector, and greater incentive for care providers to stay in it, shares in outsourcing group Mitie surged last week when it managed to offload its two homecare businesses to a private equity buyer for £1 each – but only by pledging to hand over almost £10m for future losses and turnaround costs.

Any extra cash from the chancellor, Philip Hammond, will be welcomed by councils, but they will not be dancing in the streets. The boost is likely to be simply a bringing forward of increases set for 2018-19 and 2019-20 through the Better Care Fund, with the acceleration paid for by cuts elsewhere, and it is strongly rumoured that the Care Quality Commission, the care sector regulator, will be tasked to check how it is spent.

The chancellor, Philip Hammond, is said to be determined to find a solution to the problem of social care funding. Photograph: Daniel Leal-Olivas/AFP/Getty Images

This gives rise to a fear that ministers want the cash used mainly to take pressure off hospitals by easing the problem of delayed discharge of older people awaiting social care packages in the community. Yet a third of councils’ social care spending goes on support for people with learning disabilities, whose services are also “seriously under threat” in the words of the Local Government Association.

Long-term reform of social care funding therefore remains vital. Hammond is expected to commit to this and both he and Theresa May are said to be determined to find a solution to a problem that has thwarted all governments of the past 20 years, despite a series of reviews and inquiries in that time.

The Dilnot cap, an idea recommended by economist Sir Andrew Dilnot’s review in 2011 and due to be set at personal liability for no more than £72,000 lifetime care costs, may remain in play. But under consideration, too, may be the suggestion of a “care Isa” to encourage people to save to meet their own costs, a guarantee of a set amount of free care for all and even retrospective payment of costs through an inheritance levy – despite its politically explosive “death tax” connotations.

A small Cabinet Office team has been working up an options paper for ministers. It will, we can be sure, say there is no easy answer.